Solving mathematical problems especially Calculus regarding derivative and integration sometimes poses difficulty especially for first timers. But according to experts, mathematical solving skills can easily be acquired through frequent exercises and practice solving problems. In these section, let me provide you with more examples that may help you in better understanding of this topic.

First Order Derivatives

Example #1

Find the first order derivative of the following function.

f(x)= \frac{x^{2}+bx}{x}

Quotient rule suggests that

f'(x)

=

\frac{x \cdot D_{x}(x^{2}+bx)-(x^{2}+bx)\cdot D_{x}(x)}{x^{2}}

=

\frac{x \cdot (2x+b)-(x^{2}+bx)\cdot (1)}{x^{2}}

=

\frac{x \cdot (2x+b)-x(x +b) }{x^{2}}

=

\frac{x [ (2x+b)-(x +b)] }{x^{2}}

=

\frac{ 2x+b-x +b }{x}

=

\frac{2x-x}{x}

=

1.

That was a lengthy solution, isn't it? But note that had we simplified the function first, the solution would have been very easy. We may even skip the use of quotient rule. Here's how,